154,717 research outputs found
Tree-Independent Dual-Tree Algorithms
Dual-tree algorithms are a widely used class of branch-and-bound algorithms.
Unfortunately, developing dual-tree algorithms for use with different trees and
problems is often complex and burdensome. We introduce a four-part logical
split: the tree, the traversal, the point-to-point base case, and the pruning
rule. We provide a meta-algorithm which allows development of dual-tree
algorithms in a tree-independent manner and easy extension to entirely new
types of trees. Representations are provided for five common algorithms; for
k-nearest neighbor search, this leads to a novel, tighter pruning bound. The
meta-algorithm also allows straightforward extensions to massively parallel
settings.Comment: accepted in ICML 201
Multi-Agent Deployment for Visibility Coverage in Polygonal Environments with Holes
This article presents a distributed algorithm for a group of robotic agents
with omnidirectional vision to deploy into nonconvex polygonal environments
with holes. Agents begin deployment from a common point, possess no prior
knowledge of the environment, and operate only under line-of-sight sensing and
communication. The objective of the deployment is for the agents to achieve
full visibility coverage of the environment while maintaining line-of-sight
connectivity with each other. This is achieved by incrementally partitioning
the environment into distinct regions, each completely visible from some agent.
Proofs are given of (i) convergence, (ii) upper bounds on the time and number
of agents required, and (iii) bounds on the memory and communication
complexity. Simulation results and description of robust extensions are also
included
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded
Decision trees usefully represent sparse, high dimensional and noisy data.
Having learned a function from this data, we may want to thereafter integrate
the function into a larger decision-making problem, e.g., for picking the best
chemical process catalyst. We study a large-scale, industrially-relevant
mixed-integer nonlinear nonconvex optimization problem involving both
gradient-boosted trees and penalty functions mitigating risk. This
mixed-integer optimization problem with convex penalty terms broadly applies to
optimizing pre-trained regression tree models. Decision makers may wish to
optimize discrete models to repurpose legacy predictive models, or they may
wish to optimize a discrete model that particularly well-represents a data set.
We develop several heuristic methods to find feasible solutions, and an exact,
branch-and-bound algorithm leveraging structural properties of the
gradient-boosted trees and penalty functions. We computationally test our
methods on concrete mixture design instance and a chemical catalysis industrial
instance
Block-Diagonal and LT Codes for Distributed Computing With Straggling Servers
We propose two coded schemes for the distributed computing problem of
multiplying a matrix by a set of vectors. The first scheme is based on
partitioning the matrix into submatrices and applying maximum distance
separable (MDS) codes to each submatrix. For this scheme, we prove that up to a
given number of partitions the communication load and the computational delay
(not including the encoding and decoding delay) are identical to those of the
scheme recently proposed by Li et al., based on a single, long MDS code.
However, due to the use of shorter MDS codes, our scheme yields a significantly
lower overall computational delay when the delay incurred by encoding and
decoding is also considered. We further propose a second coded scheme based on
Luby Transform (LT) codes under inactivation decoding. Interestingly, LT codes
may reduce the delay over the partitioned scheme at the expense of an increased
communication load. We also consider distributed computing under a deadline and
show numerically that the proposed schemes outperform other schemes in the
literature, with the LT code-based scheme yielding the best performance for the
scenarios considered.Comment: To appear in IEEE Transactions on Communication
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